Derive an expression for the optimal order quantity

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Reference no: EM13965621

Problem: Consider a retailer who purchases a product from a supplier at a cost of c per unit and resells it at a price of r per unit (r > c). Unsold units at the end of the selling season have a salvage value of v per unit (v < c). Demand over the selling season can be described by a continuous random variable with pdf f(x) and cdf F(x).

a) Derive an expression for the optimal order quantity Q* ?

b) The retailer buys the product from a supplier. The production cost to the supplier is b per unit (b < c). Provide an expression for the expected supplier profit as a function of the retailer’s order quantity Q.

c) Challenge: The supplier can choose c (the price it sells the product to the retailer) to maximize its own profit. Describe a procedure the supplier can use to determine its optimal selling price. If demand is uniformly distributed over the interval [0, 100], can you provide an expression for the optimal price?

Reference no: EM13965621

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